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Maxwell-Boltzmann Most-Probable Speed of a Gas Molecule Calculator

v_p = √(2RT / M).

Compute the most-probable speed of gas molecules from the Maxwell-Boltzmann speed distribution: v_p = √(2RT/M), where R = 8.31446 J·mol⁻¹·K⁻¹, T is the temperature in K, and M is the molar mass in kg/mol. Also reports mean speed ⟨v⟩ = √(8RT/πM) and rms speed v_rms = √(3RT/M).

Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

Inputs

K
kg/mol

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

v_p = √(2RT/M); ⟨v⟩ = √(8RT/πM); v_rms = √(3RT/M).

In depth

Compute the most-probable speed of gas molecules from the Maxwell-Boltzmann speed distribution: v_p = √(2RT/M), where R = 8.31446 J·mol⁻¹·K⁻¹, T is the temperature in K, and M is the molar mass in kg/mol. Also reports mean speed ⟨v⟩ = √(8RT/πM) and rms speed v_rms = √(3RT/M).